I want to sue New York Presbyterian Hospital for defamation of character and for pain and suffering. What category of lawyer can handle this for me?

I'm an employee of NYP and work in the Emergency Room as an Emergency Room Technician. I was just suspended for allegedly using too much force to control a violent patient. I believe the accusations brought against me are false , baseless and unfounded. At present, my Union ( 1199 SEIU ) is involved. We met with management to address this issue Thursday past. My Union delegate and the Union Organizer aren't exactly engendering confidence in me about this situation. I received a call from the Organizer Thursday evening to notify me that I've been suspended indefinitely pending further investigation. I have always believed that I was considered innocent until proven guilty....and I firmly believe that I'm innocent. I also believe that management will just fire me and the Union will do little or nothing at all to help me. We'll see.....actions will speak louder than words. My reputation is now being dragged through the proverbial "mud". As for Pain and Suffering, I'll need to sit down ...